Estimation of SEM with GARCH errors
The interdependence of financial markets combined with their volatility make the multivariate GARCH model a suitable econometric framework for analysing their behaviour. However, the non-availability of analytical derivatives in a general context and the computational heaviness resulting from a numerical calculation still represent a major hurdle for the use of such models in practical applications. In a general simultaneous equation model with multivariate GARCH errors, analytical expressions of the score, the Hessian and the information matrices are derived and used for implementing QML and GMM estimation procedures. The asymptotic variances of these estimators are obtained using the same expressions and the asymptotic superiority of GMM over QML is shown in the non-normal case. A simulation study comparing different gradient algorithms for ML as well as the finite sample behaviour of ML and GMM shows that using analytical results instead of numerical approximations in the optimisation procedure yields better results and reiterates the superiority of GMM over QML in finite samples under non-normality.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Haas, Markus & Mittnik, Stefan & Paolella, Marc S., 2008.
"Asymmetric multivariate normal mixture GARCH,"
CFS Working Paper Series
2008/07, Center for Financial Studies (CFS).
- Richard Harmon, 1988. "The simultaneous equations model with generalized autoregressive conditional heteroskedasticity: the SEM-GRACH model," International Finance Discussion Papers 322, Board of Governors of the Federal Reserve System (U.S.).
- Prucha, Ingmar R, 1985. "Maximum Likelihood and Instrumental Variable Estimation in Simultaneous Equation Systems with Error Components," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 491-506, June.
- Gita Persand & Chris Brooks & Simon P. Burke, 2003.
"Multivariate GARCH models: software choice and estimation issues,"
Journal of Applied Econometrics,
John Wiley & Sons, Ltd., vol. 18(6), pages 725-734.
- Chris Brooks & Simon Burke & Gita Persand, 2003. "Multivariate GARCH Models: Software Choice and Estimation Issues," ICMA Centre Discussion Papers in Finance icma-dp2003-07, Henley Business School, Reading University.
- Christian Hafner & Helmut Herwartz, 2008.
"Analytical quasi maximum likelihood inference in multivariate volatility models,"
Springer, vol. 67(2), pages 219-239, March.
- Hafner, C.M. & Herwartz, H., 2003. "Analytical quasi maximum likelihood inference in multivariate volatility models," Econometric Institute Research Papers EI 2003-21, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
- Hansen, Bruce E, 1994.
"Autoregressive Conditional Density Estimation,"
International Economic Review,
Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-30, August.
- Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
- Tom Doan, . "RATS programs to replicate Hansen's GARCH models with time-varying t-densities," Statistical Software Components RTZ00086, Boston College Department of Economics.
- BAUWENS, Luc & LAURENT, Sébastien & ROMBOUTS, Jeroen VK, .
"Multivariate GARCH models: a survey,"
CORE Discussion Papers RP
-1847, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Fiorentini, Gabriele & Sentana, Enrique & Calzolari, Giorgio, 2003. "Maximum Likelihood Estimation and Inference in Multivariate Conditionally Heteroscedastic Dynamic Regression Models with Student t Innovations," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 532-46, October.
- Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
- White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
- Krishnakumar, J. & Ronchetti, E., 1997. "Robust estimators for simultaneous equations models," Journal of Econometrics, Elsevier, vol. 78(2), pages 295-314, June.
- BAUWENS, Luc & HAFNER, Christian M. & ROMBOUTS, Jeroen VK, .
"Multivariate mixed normal conditional heteroskedasticity,"
CORE Discussion Papers RP
-1906, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Bauwens, L. & Hafner, C.M. & Rombouts, J.V.K., 2007. "Multivariate mixed normal conditional heteroskedasticity," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3551-3566, April.
- Luc, BAUWENS & C.M., HAFNER & J.V.K., ROMBOUTS, 2006. "Multivariate mixed normal conditional heteroskedasticity," Discussion Papers (ECON - Département des Sciences Economiques) 2006007, Université catholique de Louvain, Département des Sciences Economiques.
- BAUWENS, Luc & HAFNER, Christian & ROMBOUTS, Jeroen, 2006. "Multivariate mixed normal conditional heteroskedasticity," CORE Discussion Papers 2006012, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Turkington, Darrell A., 1998. "Efficient estimation in the linear simultaneous equations model with vector autoregressive disturbances," Journal of Econometrics, Elsevier, vol. 85(1), pages 51-74, July.
- White, Halbert & Kim, Tae-Hwan & Manganelli, Simone, 2008. "Modeling autoregressive conditional skewness and kurtosis with multi-quantile CAViaR," Working Paper Series 0957, European Central Bank.
- Engle, Robert F. & Granger, C. W. J. & Kraft, Dennis, 1984. "Combining competing forecasts of inflation using a bivariate arch model," Journal of Economic Dynamics and Control, Elsevier, vol. 8(2), pages 151-165, November.
- Engle, Robert F. & Ng, Victor K. & Rothschild, Michael, 1990.
"Asset pricing with a factor-arch covariance structure : Empirical estimates for treasury bills,"
Journal of Econometrics,
Elsevier, vol. 45(1-2), pages 213-237.
- Robert F. Engle & Victor Ng & Michael Rothschild, 1988. "Asset Pricing with a Factor Arch Covariance Structure: Empirical Estimates for Treasury Bills," NBER Technical Working Papers 0065, National Bureau of Economic Research, Inc.
- Harvey, Campbell R. & Siddique, Akhtar, 1999. "Autoregressive Conditional Skewness," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(04), pages 465-487, December.
- Fiorentini,G. & Calzolari,G. & Panattoni,L., 1995.
"Analytic Derivatives and the Computation of Garch Estimates,"
9519, Centro de Estudios Monetarios Y Financieros-.
- Fiorentini, Gabriele & Calzolari, Giorgio & Panattoni, Lorenzo, 1996. "Analytic Derivatives and the Computation of GARCH Estimates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(4), pages 399-417, July-Aug..
- repec:cup:cbooks:9780521252805 is not listed on IDEAS
- Fair, Ray C, 1970. "The Estimation of Simultaneous Equation Models with Lagged Endogenous Variables and First Order Serially Correlated Errors," Econometrica, Econometric Society, vol. 38(3), pages 507-16, May.
- Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
- Gourieroux, Christian & Monfort, Alain & Trognon, Alain, 1984.
"Pseudo Maximum Likelihood Methods: Theory,"
Econometric Society, vol. 52(3), pages 681-700, May.
- Lucchetti, Riccardo, 2002.
"Analytical Score for Multivariate GARCH Models,"
Society for Computational Economics, vol. 19(2), pages 133-43, April.
- Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February.
- Baltagi, Badi H., 1981. "Simultaneous equations with error components," Journal of Econometrics, Elsevier, vol. 17(2), pages 189-200, November.
- Ángel León & Gonzalo Rubio & Gregorio Serna, 2004. "Autoregressive Conditional Volatility, Skewness And Kurtosis," Working Papers. Serie AD 2004-13, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
- Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
When requesting a correction, please mention this item's handle: RePEc:eee:csdana:v:56:y:2012:i:11:p:3153-3181. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.